Error feedback structure for delta-sigma modulators with improved stability

ABSTRACT

An error feedback circuit includes a first summer receiving an analog input signal and a feedback signal and outputting a summed signal. A quantizer receives the summed signal and outputs a quantized output signal. A limiter receives the summed signal and outputs a limited summed signal. The limiter limits the limited summed signal to α* (maximum value of input signal), α&gt;1. A second summer receives the limited summed signal and the output signal and outputs an error signal. A filter receives the error signal and outputting the feedback signal. Typically, 1.0&lt;α&lt;2.0, more preferably 1.4&lt;α&lt;1.6. The filter has a transfer function of H 1 (z)=2z −1 −z −2 .

This is a continuation of U.S. application Ser. No. 10/969,852, now U.S.Pat. No. 6,956,513 issued Oct. 18, 2005 filed Oct. 22, 2004.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention is related to sigma delta modulators, and moreparticularly to delta-sigma modulators with improved stability at fullrange.

2. Related Art

Analog to Digital Converters (ADCs) are well known in the art forconverting an analog input voltage into a digital output signal as anumber of bits. Normally there is a linear correlation between an inputvoltage and a digital output value.

So-called Delta-Sigma ADCs are known in the art, which use anoversampling approach to convert the input analog signal, usingintegrators, comparators and digital filters, into a digital outputsignal. Description of this type of ADC and some embodiments can befound, e.g., in “Delta-Sigma Data Converters: Theory, Design, andSimulation,” by Steven R. Norsworthy (1996).

The advantage of Delta-Sigma ADCs is its insensitivity to imperfectionsand tolerances of the analog part of the ADC.

FIG. 1 illustrates a conventional error feedback (EFB) structure used inDelta-Sigma modulators. As shown in FIG. 1, an input signal X isreceived at a summer 102, and is inputted to a quantizer 104. Thequantizer 104 outputs an output signal Y, which is also fed back to asecond summer 106, together with the signal from the first summer 102.The second summer 106 outputs an error signal e, which is inputted intoa filter 108 having a transfer function H₁. The output of filter 108 isthen fed back to the first summer 102. The transfer function of theoutput is given by:Y(z)=X(z)+[1−H ₁(z)]*E(z)  (Eq. 1)where H₁(z) is the filter 108 transfer function, and Y, X and E are thez-transforms of the output y, the input x, and the quantization error eof the modulator. As shown in Eq. 1, the noise transfer function of theerror feedback modulator is 1−H₁(z). To achieve second order noiseshaping, the feedback filter transfer function can be selected asH₁(z)=2z⁻¹−z⁻², which results in the second order noise shaping1−H₁(z)=(1−z⁻¹)². The transfer function H₁ of filter 108 thus givessecond order noise shaping of the error signal.

The error feedback modulator has a relatively low cost of hardware andlow power consumption, and, therefore, has been widely used in thelow-power applications, such as digital voice and audio. This errorfeedback modulator, however, is subject to overflow when the modulatoris over-driven. In another words, when the input is close to or greaterthan the full-scale (Fs) of the input, the quantization error −e in FIG.1 becomes unbounded, driving the modulator towards oscillation andinstability. In other words, the structure shown in FIG. 1, as notedabove, has a stability problem when the input X is close to full scale(Fs). This results in extremely poor signal-to-noise plus distortionratio (SNDR). To prevent overflow, a limiter has to be used, as shown inFIG. 2 (see generally S. R. Norsworthy, R. Schier and G. C. Temes,“Delta-Sigma Data Converters: Theory, Design, and Simulations,” IEEEPress, New York, 1997; P. Naus et al., “A CMOS Stereo 16-bit D/AConverter for Digital Audio,” IEEE Trans. on Solid-State Circuits, pp.390 –395, vol. 22, no. 3, June 1987).

The quantizer 104 digitizes an analog voltage into a number of levels.For example, a one-bit quantizer, for an input voltage that is greaterthan zero, outputs a +1. For an input that is less than zero, theone-bit quantizer outputs −1. An N level quantizer divides the fullscale (typically between −Fs and +Fs) into N levels, and outputs adiscrete value accordingly. For example, for a three level quantizer,with full scale ranging from −1 volt to +1 volt, the quantizer willoutput discrete values at −0.5 and +0.5.

The output of the quantizer 104 introduces a quantization error, whichmay be fairly large. Therefore, the filter 108 is necessary to shape thefrequency response. The fewer levels of quantization, the greater thequantization error.

FIG. 2 illustrates a modification of the circuit of FIG. 1. Themodification includes the addition of a limiter 202 in the feedbackpath. The conventional value for the limiter is typically full scale(Fs) voltage, in other words, the limiter 202 does not permit thevoltage in that particular feedback path to go above full scale.

The limiter transfer characteristic is shown in FIG. 3. The output ofthe limiter is saturated to full-scale (Fs) when the input of thelimiter exceeds the Fs digital codes. When the modulator is overdriven,the error −e is bounded since both inputs are bounded, therefore, themodulator can be bring back to its stability when the modulator input isback to the normal range.

With the addition of the limiter 202, the inputs to the summer 106 arebounded, thereby reducing instability and oscillation of the output Y.FIG. 3 shows the transfer function of a conventional limiter 202. Asshown in FIG. 3, once the input reaches a certain value, normally Fs,the output is flat at Fs as well.

The instability of the structure such as that shown in FIG. 1 when theinput X approaches full scale is easily seen at the output Y, which doesnot reflect the input when the input is close to Fs. FIG. 4 shows aspectrum of the output Y, using a circuit of FIG. 2. As may be seen inFIG. 4, with an input of 2 KHz, strong harmonics are observed at 6 KHz,10 KHz, 14 KHz, 18 KHz, etc. When a perfect sine wave is clamped orsaturated into a trapezoid shape (i.e., “flat on the top”), its spectrumcontains not only the component at the fundamental frequency (i.e., theoriginal input frequency), but also significant 2^(nd) order components(at twice the fundamental frequency), 3^(rd) order components (threetimes the fundamental frequency) and other higher order harmonics. Thespectrum shown in FIG. 4 contains components not only the fundamentalfrequency of 2 KHz, but also higher-order harmonics of 3^(rd) order (at6 KHz), 5^(th) order (at 10 KHz), 7^(th) order (at 14 KHz), etc. This isextremely undesirable, and represents distortion and nonlinearities.

However, the inventor has discovered that such a limiter 202 asdescribed above is not optimal, because it saturates too early. Thisintroduces unnecessary distortions and non-linearities into the outputof the error feedback modulator.

Accordingly, there is a need in the art for a Delta-Sigma modulator withlower distortion.

SUMMARY OF THE INVENTION

The present invention relates to an error feedback structure forDelta-Sigma modulators with improved stability that substantiallyobviate one or more of the disadvantages of the related art.

More particularly, in an exemplary embodiment of the present invention,an error feedback circuit includes a first summer receiving an analoginput signal and a feedback signal and outputting a summed signal. Aquantizer receives the summed signal and outputs a quantized outputsignal. A limiter receives the summed signal and outputs a limitedsummed signal. The limiter limits the limited summed signal to α* (fullscale input signal, i.e., the maximum value that the input signal canhave), α>1. A second summer receives the limited summed signal and theoutput signal and outputs an error signal. A filter receives the errorsignal and outputting the feedback signal. Typically, 1.0<α<2.0, morepreferably 1.4<α<1.6. The filter has a transfer function ofH₁(z)=2z⁻¹−z⁻².

Additional features and advantages of the invention will be set forth inthe description that follows, and in part will be apparent from thedescription, or may be learned by practice of the invention. Theadvantages of the invention will be realized and attained by thestructure particularly pointed out in the written description and claimshereof as well as the appended drawings.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and areintended to provide further explanation of the invention as claimed.

BRIEF DESCRIPTION OF THE FIGURES

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this specification, illustrate embodiments of the invention andtogether with the description serve to explain the principles of theinvention. In the drawings:

FIG. 1 illustrates a conventional error feedback (EFB) structure used inDelta-Sigma modulators.

FIG. 2 shows the addition of a limiter to the circuit of FIG. 1.

FIG. 3 shows the conventional limiter transfer characteristic.

FIG. 4 shows a spectrum of the output of the circuit of FIG. 2.

FIG. 5 illustrates the transfer function characteristics of a limiter ofthe present invention.

FIG. 6 illustrates the frequency response of the output using thelimiter of the present invention.

FIG. 7 illustrates an error feedback modulator using the limiter of thepresent invention.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to embodiments of the presentinvention, examples of which are illustrated in the accompanyingdrawings.

The conventional technique to prevent the overflow can be furtherimproved. There is a optimal scaling factor 1<α<2, that yields betterSNDR. The associated limiter transfer characteristic is shown in FIG. 5.FIG. 7 illustrates an error feedback modulator using a limiter 702, withthe scaling factor α. The other components of the error feedbackmodulator are similar to those shown in FIG. 2.

FIG. 5 illustrates the transfer function characteristics of the limiter702 of the present invention. As may be seen from FIG. 5, rather thanlimiting the voltage in its feedback path at Fs (full scale, i.e., themaximum value that the input signal can have), the limiter 702 of thepresent invention limits it at some value greater than Fs, in otherwords α×Fs. The parameter α is typically between 1.0 and 2.0, morepreferably between 1.3 and 1.7, more preferably still between 1.4 and1.6.

In other words, the linear range has been extended from (−Fs to +Fs) to(−α*(Fs) to +α*(Fs)). Thus, the limiter 702 with a transfer functioncharacteristic shown in FIG. 4 more accurately reflects the input X,while still performing the limiting function.

It will be appreciated that with α approaching 1.0, the effect of theinvention will be less and less, since the input X will saturate earlierand earlier. On the other hand, with α approaching about 2.0, thelimiting function of the limiter becomes moot, and there is greaterlikelihood of oscillation and instability. Thus, a value of α ofapproximately 1.5 is believed to be optimal.

If α is too big (greater than 2), the limiter 702 becomes ineffective,the quantization error −e becomes unbounded, and the modulator isunstable. If α is too small (close to 1), the limiter 702 saturates thesignal that is still in the linear range, results in large distortionand low SNDR. From computer simulations, it was found that α≅1.5 givesthe best result. Table 1 below shows the measurement results from a testchip. The output SNDR of the modulator using the invention (α=1.5) isalways better than using a conventional limiter 202.

TABLE 1 SNDR comparison for a full-scale sine input with various inputfrequencies. Input frequency 0.5 KHz 1 KHz 2 KHz 3 KHz SNDR forconventional 15.8 dB 16.5 dB 17.8 dB 18.6 dB circuit SNDR for the 37.0dB 46 dB 62.5 dB 55 dB invention

As the above tables shows, the present invention allows a dramaticreduction in non-linearity. (SNDR is a parameter that is normally usedto measure the performance of an error feedback modulator.)

FIG. 6 illustrates the frequency response of the output Y using thelimiter 702 of the present invention, where the FFT demonstrates muchlower distortion (as evident from much smaller harmonics in the FFT). Asshown in FIG. 6, particularly in comparison with FIG. 4, the harmonicsare dramatically reduced, thereby reducing non-linearities anddistortions.

CONCLUSION

It should also be appreciated that various modifications, adaptations,and alternative embodiments thereof may be made within the scope andspirit of the present invention. The invention is further defined by thefollowing claims.

1. A method for improving stability of delta-sigma modulation process,comprising: (a) receiving an analog input signal and a feedback signal;(b) summing the received analog and feedback signal to produce a summedsignal, wherein the summed signal is limited such that the absolutevalue of a limited summed signal has the value α*(maximum value of theinput signal), α>1; (c) quantizing the summed signal and outputting aquantized output signal; (d) generating an error signal by summing thelimited summed signal and the quantized output signal, and (e)performing second order filtering of the error signal to produce thefeedback signal.
 2. The method of claim 1, wherein 1.0<α<2.0.
 3. Themethod of claim 1, wherein 1.4<α<1.6.
 4. The method of claim 1, furthercomprising performing the second order filtering using a transferfunction H₁(z)=2z⁻¹−z⁻².